A polynomial transform approach to transmultiplexing

In this paper, we introduce a new algorithm for the implementation of uniform digital bandpass filter banks. This technique first uses a conventional filter breakdown process to convert a set of fast bandpass filters into a set of slow bandpass filters of reduced length, plus an odd-time DFT. The slow bandpass filters are computed by DFTs, and it is shown that the combination of these DFTs with the odd-time DFT yields a simple algorithm using an inverse polynomial transform. with this method, almost all operations reduce to FFT-type calculations which can be implemented efficiently in signal processors. Moreover, the polynomial transform approach reduces significantly the computational complexity over conventional techniques. The polynomial implementation of digital filter banks may be used in a number of applications such as TDM-FDM transmultiplexers, speech compression systems and spectrum analyzers.